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I guess a different way of asking this question is whether or not all parts of a character have a radical. Also, why is this info useful?
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xiaohouzi79♦Nov 20 '13 at 0:19

As a matter of fact, some characters use their first stroke as a radical in the Xinhua (New Chinese) Dictionary. Besides, there's usually an index ordered by the number of strokes to facilitate the lookup process of a hard-to-break-down character.
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phoeagonNov 20 '13 at 4:56